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Subject:  Linear Algebra

Eigenvalues and eigenvectors of [[4, 1], [2, 3]]

Find the eigenvalues from the characteristic polynomial and an eigenvector for each.

Answer λ1 = 5, λ2 = 2; λ=5 → v=(0.707107, 0.707107); λ=2 → v=(-0.447214, 0.894427)

Solution

  1. Matrix A 2×2 [[4, 1], [2, 3]]
  2. Characteristic polynomial det(A − λI) = λ² − tr(A)·λ + det(A) = λ² − 7·λ + 10
  3. Eigenvalues λ1 = 5, λ2 = 2
  4. Eigenvector λ = 5: v = (0.707107, 0.707107)
  5. Eigenvector λ = 2: v = (-0.447214, 0.894427)

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